Download Boy, Do I Love Base 10

Project 2
Boy, Do I Love Base 10
Purpose: Investigate the base 10 system.
Outline: After a brief review of numbering systems, we will explore the Egyptian system and compare it to the
base 10 system.
Content Objectives: To dive deeper into our system, and investigate why things work the way they do.
Materials Needed: Random number generator (0-9).
Instructions: Go through the following exercises, and answer the given questions completely. You must show
all work.
Background:
Ancient Egyptian Number System:
 Ancient Egyptian hieroglyphics (3400 BC) is an additive system, which uses the following symbols

They would express 321 as
Our Number System
 Our method is called Hindu-Arabic invented by the Hindus sometime before 600AD and refined over time.
 It uses 10 symbols (0 1 2 3 4 5 6 7 8 9) or digits
 It is grouped by tens (also known as a decimal system), being that each digit has a place value
 To see how place value works, each number can be broken down into what is called expanded form.
 For example, 542 = 5 102  4  101  2  100
Terms:
 The term natural numbers refers to { 1, 2, 3, 4 …}.
 The term whole numbers refers to { 0, 1, 2, 3, 4 …}.
 An integer refers to a value above that can also be negative, i.e. { … –3, –2, –1, 0, 1, 2, 3 …}.
Part A: Exploring the Egyptian System
1. Together we will go to the site http://gwydir.demon.co.uk/jo/numbers/egypt/intro.htm and see how to
express the following numbers in this system. Write the solution on the line.
52
567
3,671
1,000,021
21,000
59
2. Adding two numbers is straightforward in this system, and involves regrouping, if necessary. Let’s
explore by first representing both numbers in the middle column.
5+4
10 + 5
21 + 13
95 + 12
220 + 87
Then, regroup if there are more than 10 of any symbol, and write the final answer in the last column.
Part B: How Can I Use that Method in Our Number System?
3. Rewrite the following numbers in expanded form
213 = 2 (100) + 1(10) + 3(1)
3,549
1,235,608
45,000
4. We sometimes take for granted the ease of our positional system. When adding, let’s first represent both
numbers in the middle column using expanded form.
21 + 13
2 (10) + 1
1(10) + 3
3(10) + 4 = 34
15 + 32
95 + 12
220 + 87
Then, regroup if needed, and write the final answer in the last column.
PART C: Place Value Bingo
Millions
One
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
PART D: Why Does the Multiplication Algorithm Work?
5. When we multiply (long hand) we use the procedure below
6. Explain why we ‘indent’ the 63?
Ones
.
Tenths
Hundredths
Thousandths